Algorithms for the solution of internal variable problems in plasticity

The null stress (s 33 = 0) and incompressibility (J = 1) conditions in finite strain elasto-plastic shell analysis are studied in closed-form and implemented with a variant of the combined control by Ritto-Corrêa and Camotim. Coupling between constitutive laws and shell kinematics results from the satisfaction of either of the conditions; nonlocality results from the coupling. We prove that the conditions are, in general, incompatible. A new thickness-deformable is studied in terms of kinematics and strong-ellipticity. The affected continuum laws are derived and, in the discrete form, it is shown that thickness degrees-of-freedom and enhanced strains are avoided: a mixed displacement-shear strain shell element is used. Both hyperelastic and elasto-plastic constitutive laws are tested. Elasto-plasticity follows Lee's decomposition and direct smoothing of the complementarity condition. A smooth root finder is employed to solve the resulting algebraic problem. Besides closed-form examples, numerical examples consisting of classical and newly proposed benchmarks are solved.

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“…[39]). Solutions based on the dual formulation are now firmly established both with predictor/corrector [28] and Shur-based methodologies [32].…”

Section: Introductionmentioning

confidence: 93%

“…In the linearization of elasto-plasticity only sub-differentials are obtained for points in the yield surface and the overall problem remains non-smooth [39]. For a sequence of global iterations, a given quadrature point can have a sequence of loading/unloading or reloading/unloading states.…”

Section: Introductionmentioning

confidence: 99%

Finite strain plasticity, the stress condition and a complete shell model

Areias

Ritto‐Corrêa

Martins³

2009

Comput Mech

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“…Such a decomposition corresponds to the mechanical assumption that the elastic behaviour does not depend on the evolution of inelastic phenomena and has been usually adopted in literature concerning local and gradient plasticity, see e.g. Lubliner (1990) Reddy and Martin (1991), Simo et al (1988), Str€ omber andRistinmaa (1996), and Svedberg and Runesson (1998).…”

Section: Nonlocal and Gradient Plasticitymentioning

confidence: 98%

Nonlocal and gradient rate plasticity

Sciarra

2004

International Journal of Solids and Structures

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“…It is worth noting that, in the field of local plasticity, formulations and algorithms presented in Bird and Martin (1990) and Reddy and Martin (1991) provide a dual viewpoint of the ones pursued in Ortiz and Popov (1985) and Simo and Govindjee (1991) since, in the former papers, variational and algorithmic aspects are based on the evolution law expressed in terms of the dissipation functional and in the latter papers the elastoplastic problem is expressed in terms of the convex yield function, normality rule and plastic multiplier.…”

Section: Introductionmentioning

confidence: 99%

Variational formulations, convergence and stability properties in nonlocal elastoplasticity

Sciarra

2008

International Journal of Solids and Structures

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A thermodynamically consistent formulation of nonlocal plasticity in the framework of the internal variable theories of inelastic behaviors of associative type is presented. A family of mixed variational formulations, with different combinations of state variables, is provided starting from the finite-step nonlocal elastoplastic structural problem. It is shown that a suitable minimum principles provides a rational basis to exploit the iterative elastic predictor-plastic corrector algorithm in terms of the dissipation functional. A sufficient condition is proved for the convergence of the iterative elastic predictor-plastic corrector algorithm based on a suitable choice of the elastic operator in the prediction phase and a necessary and sufficient condition for the existence of a unique solution (if any) of the nonlocal problem at hand is then provided. The nonlinear stability analysis of the nonlocal problem is carried out following the concept of nonexpansivity proposed in local plasticity

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Algorithms for the solution of internal variable problems in plasticity

Cited by 55 publications

References 18 publications

Finite strain plasticity, the stress condition and a complete shell model

Finite strain plasticity, the stress condition and a complete shell model

Nonlocal and gradient rate plasticity

Variational formulations, convergence and stability properties in nonlocal elastoplasticity

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